Taking into account the unitary operation \(\hat{U}_7\) , our MCF-based devices can implement finite sets of inequivalent rank-1 POVM elements, as we explain next. We consider the scenario depicted in Fig. REF , where a POVM is realized acting upon an input quantum state \(|\Psi \rangle \)  of dimension \(d\)  lower than \(D\) . In our experiment, \(D=7\)  corresponds to all the spatial modes available in the \(7\times 7\)  MBS. Then, the remaining \(D-d\)  cores define the ancilla system used to extend the Hilbert space dimension of the input state. Likewise, according to Neumark's dilation theorem [1]}, the action of the POVM is obtained by performing a projective measurement over the total system (i.e., detecting all cores). The total number of feasible POVMs we can implement is determined by the number of subsets of \(d\)  elements chosen from a set of \(D\)  elements, that is
\(\binom{D}{d}=\frac{D!}{d!(D-d)!}.\) 
